We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level bidirectional A* search algorithm. In high-level reachability analysis, a backward reachable tube (BRT) concerning vehicle dynamics is computed by the HJ analysis and it intersects with a safe set to get a safe reachable set. The safe set is defined by constraints of positive signed distances for obstacles in the environment and computed by solving QP optimization problems offline. For states inside the intersection set, i.e., the safe reachable set, the computed backward reachable tube ensures they are reachable subjected to system dynamics and input bounds, and the safe set guarantees they satisfy parking safety with respect to obstacles in different shapes. For online computation, randomized states are sampled from the safe reachable set, and used as heuristic guide points to be considered in the bidirectional A* search. The bidirectional A* search is paralleled for each randomized state from the safe reachable set. We show that the proposed two-level planning algorithm is able to solve different parking scenarios effectively and computationally fast for typical parking requests. We validate our algorithm through simulations in large-scale randomized parking scenarios and demonstrate it to be able to outperform other state-of-the-art parking planning algorithms.

翻译：我们提出了一种名为Hamilton-Jacobi双向A*（HJBA*）的快速规划架构，用于解决一般性紧凑泊车场景。该算法采用双层结构，上层基于Hamilton-Jacobi（HJ）可达性分析，下层采用双向A*搜索算法。在上层可达性分析中，通过HJ分析计算考虑车辆动力学的后向可达管（BRT），并与安全集合相交得到安全可达集合。安全集合由环境中障碍物的正有符号距离约束定义，并通过离线求解二次规划（QP）优化问题获得。对于交集中的状态（即安全可达集合），计算所得的后向可达管确保这些状态在系统动力学和输入约束下可达，同时安全集合保障其满足不同形状障碍物的泊车安全性。在线计算阶段，从安全可达集合中随机采样状态，并作为启发式导向点纳入双向A*搜索；针对每个随机状态，双向A*搜索并行执行。实验表明，所提出的双层规划算法能够有效求解多种泊车场景，并在典型泊车请求中实现快速计算。通过大规模随机泊车场景的仿真验证，该算法的性能优于其他先进泊车规划算法。